| 摘 要： | In this paper we introduce a family of multivariate distributions,which consists of scale mixtures of symmetrized Dirichlet distributions,This family is a symmetrization of multivariate Liouville distributions and contains the well-known spherically symmetric distributions as a special case.The basic properties of this family such as stochastic representation,probability density functions,marginal and conditional distributions and components'independence are studied.A criterion of the invariance of statistics is also given.
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